DPMS: An ADD-Based Symbolic Approach for Generalized MaxSAT Solving

TL;DR

DPMS introduces a novel ADD-based dynamic programming framework capable of solving generalized MaxSAT problems with hybrid constraints, outperforming existing methods on certain challenging instances.

Contribution

The paper presents a new ADD-based dynamic programming approach for generalized MaxSAT with hybrid constraints, enabling native handling of non-CNF formulas and broad problem generalizations.

Findings

DPMS can solve certain hybrid MaxSAT problems efficiently.

It scales well on low-width instances.

Outperforms existing algorithms on some benchmarks.

Abstract

Boolean MaxSAT, as well as generalized formulations such as Min-MaxSAT and Max-hybrid-SAT, are fundamental optimization problems in Boolean reasoning. Existing methods for MaxSAT have been successful in solving benchmarks in CNF format. They lack, however, the ability to handle 1) (non-CNF) hybrid constraints, such as XORs and 2) generalized MaxSAT problems natively. To address this issue, we propose a novel dynamic-programming approach for solving generalized MaxSAT problems with hybrid constraints -- called \emph{Dynamic-Programming-MaxSAT} or DPMS for short -- based on Algebraic Decision Diagrams (ADDs). With the power of ADDs and the (graded) project-join-tree builder, our versatile framework admits many generalizations of CNF-MaxSAT, such as MaxSAT, Min-MaxSAT, and MinSAT with hybrid constraints. Moreover, DPMS scales provably well on instances with low width. Empirical results indicate that DPMS is able to solve certain problems quickly, where other algorithms based on various techniques all fail. Hence, DPMS is a promising framework and opens a new line of research that invites more investigation in the future.